A Bayesian Framework for the Analysis and Optimal Mitigation of Cyber Threats to Cyber-Physical Systems.

Critical infrastructures are increasingly reliant on information and communications technology (ICT) for more efficient operations, which, at the same time, exposes them to cyber threats. As the frequency and severity of cyberattacks are increasing, so are the costs of critical infrastructure security. Efficient allocation of resources is thus a crucial issue for cybersecurity. A common practice in managing cyber threats is to conduct a qualitative analysis of individual attack scenarios through risk matrices, prioritizing the scenarios according to their perceived urgency and addressing them in order until all the resources available for cybersecurity are spent. Apart from methodological caveats, this approach may lead to suboptimal resource allocations, given that potential synergies between different attack scenarios and among available security measures are not taken into consideration. To overcome this shortcoming, we propose a quantitative framework that features: (1) a more holistic picture of the cybersecurity landscape, represented as a Bayesian network (BN) that encompasses multiple attack scenarios and thus allows for a better appreciation of vulnerabilities; and (2) a multiobjective optimization model built on top of the said BN that explicitly represents multiple dimensions of the potential impacts of successful cyberattacks. Our framework adopts a broader perspective than the standard cost-benefit analysis and allows the formulation of more nuanced security objectives. We also propose a computationally efficient algorithm that identifies the set of Pareto-optimal portfolios of security measures that simultaneously minimize various types of expected cyberattack impacts, while satisfying budgetary and other constraints. We illustrate our framework with a case study of electric power grids.

Assessing the time intervals between economic recessions.

Economic recessions occur with varying duration and intensity and may entail substantial losses in terms of GDP, employment, household income, and investment spending. In this work, we propose a statistical model for the time intervals between recessions that accounts for the state of the economy and the impact of market adjustments and regulatory changes. The model uses a generalized renewal process based on the Gumbel distribution (GuGRP) in which times between consecutive events are conditionally independent. We also present a novel goodness of fit test tailored to the GuGRP that validates the use of the statistical model for the analysis of recessions. Analyzing recessions in the U.S. and Europe, we demonstrate that the statistical model characterizes well recession inter-arrival times and that the model performs better than simpler, commonly used distributions. In addition, the presented statistical model enables us to compare the adjustment processes in different economies and to forecast the occurrence of future recessions.

Asymptotic behaviour of random walks with correlated temporal structure.

We introduce a continuous-time random walk process with correlated temporal structure. The dependence between consecutive waiting times is generated by weighted sums of independent random variables combined with a reflecting boundary condition. The weights are determined by the memory kernel, which belongs to the broad class of regularly varying functions. We derive the corresponding diffusion limit and prove its subdiffusive character. Analysing the set of corresponding coupled Langevin equations, we verify the speed of relaxation, Einstein relations, equilibrium distributions, ageing and ergodicity breaking.

Correlated continuous-time random walks in external force fields.

We study the anomalous diffusion of a particle in an external force field whose motion is governed by nonrenewal continuous time random walks with correlated waiting times. In this model the current waiting time T_{i} is equal to the previous waiting time T_{i-1} plus a small increment. Based on the associated coupled Langevin equations the force field is systematically introduced. We show that in a confining potential the relaxation dynamics follows power-law or stretched exponential pattern, depending on the model parameters. The process obeys a generalized Einstein-Stokes-Smoluchowski relation and observes the second Einstein relation. The stationary solution is of Boltzmann-Gibbs form. The case of an harmonic potential is discussed in some detail. We also show that the process exhibits aging and ergodicity breaking.